Elasticity as a measure for online determination of remission points in ongoing epidemics.

The correct identification of change-points during ongoing outbreak investigations of infectious diseases is a matter of paramount importance in epidemiology, with major implications for the management of health care resources, public health and, as the COVID-19 pandemic has shown, social live. Onsets, peaks, and inflexion points are some of them. An onset is the moment when the epidemic starts. A "peak" indicates a moment at which the incorporated values, both before and after, are lower: a maximum. The inflexion points identify moments in which the rate of growth of the incorporation of new cases changes intensity. In this study, after interpreting the concept of elasticity of a random variable in an innovative way, we propose using it as a new simpler tool for anticipating epidemic remission change-points. In particular, we propose that the "remission point of change" will occur just at the instant when the speed in the accumulation of new cases is lower than the average speed of accumulation of cases up to that moment. This gives stability and robustness to the estimation in the event of possible remission variations. This descriptive measure, which is very easy to calculate and interpret, is revealed as informative and adequate, has the advantage of being distribution-free and can be estimated in real time, while the data is being collected. We use the 2014-2016 Western Africa Ebola virus epidemic to demonstrate this new approach. A couple of examples analyzing COVID-19 data are also included.

El punto de remisión de una epidemia localizado por su elasticidad: aplicación a la primera ola del COVID-19 en Chile / The remission point of an epidemic identified by elasticity. application to the first wave of covid-19 in Chile

INTRODUCCIÓN. La detección de cambios en las características de un proceso aleatorio, conocido como el problema del cambio, se ha convertido en un área de investigación estadística en rápido desarrollo. La correcta y rápida detección de los cambios es relevante en muchas situaciones reales, en particular, en Epidemiología. MATERIALES Y MÉTODOS. Como nueva métrica para determinar el momento efectivo de remisión de una epidemia (momento del cambio), se utiliza el concepto de elasticidad de una distribución de probabilidad, y se aplica a la reciente pandemia COVID-19 en Chile. RESULTADOS. La aplicación evidencia que existe una demora entre el día "pico" o día con el mayor número de casos, con el de "remisión" identificado por la elasticidad. En ese lapso temporal, entre pico y remisión, no deben suavizarse las medidas de control de la epidemia. Se obtiene una diferencia de 20 días entre los puntos de remisión de las series de contagios y muertes. Esta cifra puede interpretarse como una estimación de la supervivencia para los fallecidos durante la primera ola de COVID-19 una vez detectada en ellos la enfermedad. La comparación de los resultados de la aplicación con la de otros países sudamericanos muestra en ellos idéntico resultado que el observado en Chile, si bien con tiempos de demora entre pico y punto de remisión sensiblemente mayores. DISCUSIÓN. La medida usada en este trabajo es fácil de comunicar, no exige la formulación previa de hipótesis sobre el comportamiento de los datos y puede ser aplicada en tiempo real, tal y como se van conociendo los datos. Estas características de fácil aplicabilidad e interpretación, generando resultados razonables, la hacen atractiva e interesante para el estudio del cambio en series epidemiológicas.

INTRODUCTION. Detecting changes in the evolution of a random process, known as the problem of change, has become a quickly developing area of statistical research. The correct and rapid detection of changes is relevant in many real-life situations, particularly in epidemiology.MATERIALS AND METHODS. As a new metric to time-locate the moment of remission of an epidemic (moment of change), the concept of the elasticity of a probability distribution is applied to the recent COVID-19 pandemic in Chile.RESULTS. The application shows that there is a delay between the "peak" day, or day with the highest number of cases, and the "remission" day as identified by elasticity. In this period, between peak and remission, the epidemic control measures should not be relaxed. A difference of 20 days is obtained between the remission points of the series of infections and deaths. This figure can be interpreted as an estimate of survival time for those diagnosed with the disease who subsequently died during the first wave of COVID-19. Comparing the results of the application with that of other South American countries, we observe the same result as that attained for Chile, although with significantly longer delay times between the peak and the point of remission.DISCUSSION. The measure used in this study is easy to communicate, does not require the prior formulation of hypotheses about the behaviour of the data and can be applied in real time, as and when the data is known. These characteristics of easy applicability and interpretation, generating reasonable results, make the application convenient for the study of change in epidemiological series